\section{Background}
\label{sec:Background}

PCIR advocates assume that health care providers are wasteful and inefficient, providing more services than needed to generate more income. PCIR advocates believe that fee for service providers over-test, over-diagnose, and over-treat patients and implementing PCIR encourages providers to become less inefficient. PCIR critics fear that risk assuming providers will under-test, under-diagnose, and under-treat patients.(2-6,24)
Unethical, profit maximizing, providers exist in both systems, maximizing net income by delivering excessive care under fee for service and inadequate care under PCIR. These unethical providers harm patients by exposing them to excessive testing and intervention or by failing to diagnose and treat them as early as they could.

There is also widespread misunderstanding about insurance. Jonas (24) (See footnote pg 9) suggests that health insurance is not ``real insurance'' because people will use all their benefits eventually. Correcting misconceptions about insurance and PCIR is difficult because few people recognize that the most important consideration is insurer size. With regard to Jonas' concern, we note that ``whole life'' insurance always pays full benefits but it is the timing of premiums and benefits that determines feasibility.(19,16,17,25)

Risk managers, health policy analysts and providers need to understand insurance rate making and operating results. This paper begins building these capabilities. We begin by avoiding faulty assumptions about waste and inefficiency that hide the inefficiency of PCIR, concentrating instead; on the effect insurer size has on insurer's operating results. 	

We can demonstrate the flaws in PCIR with a simple model and familiar statistical tools if we assume that the health care (finance) systems are already efficient. We then analyze how portfolio size affects operating results for large and small insurers (small risk assuming health care providers), immediately before and after the implementation of PCIR.

The key to insurance is the variation in insurer's loss ratios as functions of insurer portfolio size.(10,17,18,26,27) Many risk managers assume that because both large and small insurers have identical ``expected loss ratios'' when selecting policyholders at random, they should have identical probabilities of outcomes at loss ratios other than the expected values. To demonstrate that this is not true we make modest assumptions about a large ``Paradigm Insurer'' (PI), using the Central Limit Theorem to make inferences about other insurers.(28) 

We cannot account for all the risk insurers' face. Instead, we focus on the routine variation in insurer's fortunes. A pandemic would sap the strength of any health insurer, and most would not survive even a fairly modest epidemic. Our model focuses on insurer's non-cataclysmic risk exposure.
